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There is a discussion of analogy and similarity (and other terms referring to alikeness here at M-W. The gist is this:

Similar refers to things that are somewhat alike, and those characteristics that are alike are the same in a direct comparison. For example, you might use "similar" to describe how a man had a remarkable likeness to his father.

Analogous refers to parallelism or correspondence. For example, the heart is analogous to a pump, or an airplane's joystick is somewhat analogous to the reins on a horse.